• Instructor's Guide for D. Poole's Linear Algebra, Brookes/Cole, (2005), ISBN 0-534-99861-5.

  • Instructor's Guide for D. Poole's Linear Algebra Second edition, Brooks/Cole | Cengage Learning, (2011) online access only.

  • The geometry of minimal shape-preserving projections, with B.L. Chalmers, Computers Math. Applic. 30(1995), No. 3-6, 277-281.


  • Codimension one minimal projections onto the quadratics: J. Approx. Theory, 85(1996), 27-42.


  • A farthest-point characterization of the relative Chebyshev center, with R. Huotari, Bull. Austral. Math. Soc., 54(1996), 27-33.


  • Minimal shape-preserving projections onto     $\Pi_n$$$, with B.L. Chalmers, Numer. Funct. Anal. and Optimiz., 18(1997), 507-520.


  • The Bernstein operator is the closest positive operator to a projection, with B.L. Chalmers, D. Leviatan, Approximation Theory IX, Volume 1: (Nashville, TN, 1998), 75-82, Vanderbilt University Press.


  • Existence of shape preserving A-action operators, with B.L. Chalmers, Rocky Mountain J. Math., 28(1998), No. 3, 813-833.


  • Optimal interpolating spaces preserving shape, with B.L. Chalmers, D. Leviatan, J. Approx. Theory, 98(1999), 354-373.

  • On $j$-convex preserving interpolation operators, J. Approx. Theory 104(2000), 77-89.


  • Constrained optimal location, with R. Huotari, Numer. Funct. Anal. and Optimiz. 22(1&2)(2001), 69-78.


  • Optimal location with convex constraints, with R. Huotari and J. Ribando, Approximation Theory X: Abstract and Classical Analysis, (C.Chui, L. Schumaker, J. Stoeckler eds.), Vanderbilt Press (2002), 239-246.


  • On a constrained optimal location algorithm, with R. Huotari, J. of Computational Analysis and Applications, 5, No. 1, (2003).


  • Simplicial cones and the existence of shape-preserving cyclic operators, Linear Algebra and its Applications, 375 (2003), 157-170.


  • Codimension-one minimal projections onto Haar subspaces, with G. Lewicki, J. Approx. Theory, 127 (2004), 198-206.


  • A characterization and equations for minimal shape-preserving projections, with B. Chalmers and D. Mupasiri, J. Approx. Theory, 138 (2006), 184 - 196.


  • A note on the existence of shape-preserving projections, with D. Mupasiri, Rocky Mountain J. Math., 37(2007), No. 2, 573-585.


  • Minimal shape-preserving projections onto $\Pi_n$: Generalizations and Extensions, with G. Lewicki, Numer. Funct. Anal. and Optimiz., 27(2006), No. 7-8, 847-874.


  • A Lower Bound of the Strongly Unique Minimal Projection Constant of $l_{\infty}^n$, $n\geq 3$, with W. Odyniec, J. Approx. Theory, 145(2007), No. 1, 111-121.


  • Minimal multi-convex projections, with G. Lewicki, Studia Math. 178(2007), No. 2, 99-124.


  • On Three Forgotten Results of S. Krein, N. Bogolyubov and V. Guarari with Applications to Bernstein Operators, with W. Odyniec, Vestn. Syktyvkar Unin., 1(2007), 16-24.


  • On the difficulty of preserving monotonicity via projections and related results, with D. Mupasiri, Jaen J. Approx., 2 No. 1 (2010), 1-12.


  • Shape-preserving projections in tensor product spaces, with G. Lewicki, J. Approx. Theory, 162 No. 5 (2010), 931-951.


  • Shape-preserving projections in low-dimensional settings and the $s$-monotone case, with I. Shevchuk, Ukrainian Math. J., 5(2012), 674-684.


  • Yet another generalization of a celebrated inequality of the Gamma function, with E.M. Garcia-Caballero and S.G. Moreno, Amer. Math. Monthly 120 (2013), 821.


  • New Viete-Like Infinite Products of Nested Radicals with Fibonacci and Lucas Numbers, with E.M. Garcia-Caballero and S.G. Moreno, The Fibonacci Quarterly, 52(2014), no. 1, 27-31.


  • The Golden Ratio and Viete's Formula, with E.M. Garcia-Caballero and S.G. Moreno, Teach. Math. Comp. Sci., 12(2014), no. 1, 43-54.


  • A complete view of Viete-like infinite products wwith Fibonacci and Lucas Numbers, with E.M. Garcia-Caballero and S.G. Moreno, Applied Mathematics and Computation, 247(2014), 703-711.


  • A Note on the Existence of Real Two-dimensional Symmetric Subspaces of $L^p[-1,1]$, with G. Lewicki and W. Wood, Real Analysis Exchange, 45(2020), no. 2, 1-16.


  • The Chalmers-Metcalf Operator and Minimal Extensions, with G. Lewicki, J. Funct. Analysis 280(2021), no. 1, 1-30.


  • Codimension 1 minimal projections onto the lines in $L^p$, with G. Lewicki J. Approx. Theory, 283(2022), 105812.


  • Simultaneous Minimal Extensions on the Lines in $L^p$ and the Cubic Case , with G. Lewicki, Real Analysis Exchange, 50(2025), no. 1, 1-19.


  • Minimal Polynomial Extensions and Projections onto the Lines in $L^p[-1,1]$, with G. Lewicki, Pure and Applied Functional Analysis, 10(2025), no. 3, 565-582.


  • Extending Projections On Spaces of Even and Odd Functions in $L^p[-1,1]$, submitted for publication.


  • Minimal $L^p$ projections onto the lines, work in progress.



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