Publications with Undergraduates

The following is a list of publications by Mathematics Faculty, co-authored by undergraduate students.

Students in William and Mary's REU programs were supported by a sequence of NSF REU site grants.

Papers are listed in reverse chronological order.

* indicates an undergraduate student.

** indicates a W&M undergraduate student

  • T. Leake*, B. Lins  and I. M. Spitkovsky. Inverse Continuity on the Boundary of the Numerical Range, Linear and Multilinear Algebra, to appear. 
  • T. Leake*, B. Lins  and I. M. Spitkovsky. Pre-images of Boundary Points of the Numerical Range,  Operators and Matrices, to appear. 
  • T. Moran** and I. M. Spitkovsky. On almost normal matrices, Textos de Matematica, 44 (2013), 131-144.
  • C.R.Johnson, Z. Price** and I. M. Spitkovsky, The distribution of eigenvalues of doubly cyclic Z+-matrices, Linear Algebra and its Applications 439 (2013), 3576-3580.
  • R. Case, T. Dey, B. Anderson**, J. Gumz**, C. Wise**, A Study to Examine Differences in Sporting Event Direct Spending While Using Online and In Person Survey Methods. Sport Management International Journal, 9(2), (2013), 17--31.
  • R. Case, T. Dey, J. Lu**, J. Phang**,  and  A. Schwanz**, Participant Spending at Sporting Events: An Examination of Survey Methodologies. Journal of Convention and Event Tourism, 14, (2013), 21 -- 41.
  •  C.K. Li, R. Roberts** and X. Yin, Decomposition of unitary matrices and quantum gates, International Journal of Quantum Information, to appear.  arXiv:1210.7366.
  • J.Y.Jin*, J.P. Shi, J.J. Wei, and F.Q. Yi, Bifurcations of Patterned Solutions in diffusive Lengyel-Epstein System of CIMA Chemical Reaction, Rocky Mountain Journal of Mathematics, to appear.
  • D. Corey*, C. Johnson, R. Kirk* , B. Lins and I. M. Spitkovsky, Continuity properties of vectors realizing points in the classical field of values, Linear and Multilinear Algebra, to appear. 
  • D. Corey*, C. Johnson, R. Kirk* , B. Lins and I. M. Spitkovsky, The product field of values, Linear Algebra and Applications, 438 (2013), 2155--2173. 
  • J. Eldred**, L. Rodman and I. M. Spitkovsky, Numerical ranges of companion matrices: flat portions on the boundary, Linear and Multilinear Algebra, 60 (2012), 1295 -- 1311 . 
  • L. Leemis, J. Yang**, J. Drew,  Automating Bivariate Transformations, INFORMS Journal on Computing Vol. 24, No. 1, Winter 2012, pp. 1–9.
  • L. Williams**,  J.Vandenbussche, and G.X. Yu,  Equitable defective coloring of sparse planar graphs,  Discrete Math.,312(5): 957-962 (2012).
  • C. Albert**,  C.K. Li, G. Strang and G.X. Yu, Permutations as product of parallel transpositions, SIAM J. Disc. Math., 25 (2011), pp. 1412-1417.
  • W. C. Jordan-Cooley**, R. N. Lipcius, L. B. Shaw, J. Shen and J.P. Shi,Bistability in a differential equation model of oyster reef height and sediment accumulation , Journal of Theoretical Biology, 289, (2011), 1--11.
  • F. Jiang* and C. R. Vinroot, A semi-recursion for the number of involutions in special orthogonal groups over finite fields, Finite Fields and their Applications, 17, (2011), no. 6, 532--551.
  • R.Y. Sun**, J.P. Shi, Global stability of multigroup epidemic model with group mixing and nonlinear incidence rates. Applied Mathematics and Computation, 218, (2011) 280--286.
  • B. Lins, E. Einstein*,  C. R. Johnson and I. M. Spitkovsky, The ratio field of values, Linear Algebra and Applications,  434 (2011), 1119--1136.
  • T. R. Harris*, M. Mazella*, L. J. Patton,  D. Renfrew* and I. M. Spitkovsky, Numerical ranges of cube roots of the identity, Linear Algebra and Applications, 435 (2011), 2639--2657.
  • J.P. Shi, Z.F. Xie, and K. Little**, Cross-diffusion induced instability and stability in reaction-diffusion systems, Journal of Nonlinear Analysis and Computation, 1, (2011), 1, 95--119.
  • V. Forstall**,  A. Herman**,  C.K. Li, N.-S. Sze, and V. Yannello**, Preservers of eigenvalue inclusion sets of matrix products. Linear Algebra Appl. 434 (2011), no. 1, 285--293.
  • T. Dey, D.J. Phillips, and P. Steele**, Visualizing and finding minimum delay flights, Journal of Computational and Graphical Statistics, 20 (2011), 294--297.
  • M. B. Kutler* and C. R. Vinroot, On q-analogs of recursions for the number of involutions and prime order elements in symmetric groups, Journal of Integer Sequences, 13, (2010), no. 3, Article 10.3.6, 12 pp.
  • R.Y. Sun**, Global stability of the endemic equilibrium of multigroup SIR models with nonlinear incidence. Comput. Math. Appl. 60 (2010), 2286--2291.
  • R. Case, T. Dey, S.  Hobbs**,  J. Hoolachan**, and A. Wilcox**. An Examination of Sporting Event Direct Spending Patterns at Three Competitive Levels. Journal of Convention and Event Tourism, 11(2), (2010), 119 -- 137.
  • J. Hartman, A. Herman**, and C.K. Li, Preservers of eigenvalue inclusion sets, Linear Algebra Appl., 433, (2010), 1038--1051.
  • S. Clark**, C.K. Li and N.S. Sze, Multiplicative maps preserving the higher rank numerical ranges and radii, Linear Algebra Appl. 432 (2010), 2729-2738.
  • H. Seyalioglu**, L. Rodman, and I. Spitkovsky,  On common invariant cones for families of matrices,  Linear Algebra and Applications, 432(2010), 911--926.  
  • T. Crowder** and C.K. Li, Studying Genetic Code by a Matrix Approach, Bulletin of Mathematical Biology 72 (2010), 953-972.
  • J.P. Tian, K. Stone**, and T.J. Wallin**, A simplified mathematical model of solid tumor regrowth with therapies, Discrete and Continuous Dynamical Systems, supplement 2009, 771--779.
  • S. Clark**, C.K. Li,   J. Mahle** and L. Rodman, Linear preservers of higher rank numerical ranges and radii, Linear and Multilinear Algebra, 57(2009), 503--521.
  • A. Rastogi**, L. Rodman, and I. Spitkovsky, Almost periodic factorization of 2-by-2 triangular matrix functions: New cases of off diagonal spectrum, Operator Theory: Advances and Applications, 202(2009), 469--487.
  • R. Kincaid, N. Alexandrov, and M.Holroyd**, An investigation of synchrony in transport networks,'' Complexity 14, (2009) 34--43.
  • S.Day, R. Frongillo* and R. Trevino*, Algorithms for rigorous entropy bounds and symbolic dynamics, SIAM Journal on Applied Dynamical Systems 7 (2008), 1477--1506.
  • S. Clark**, C.K. Li  and L. Rodman , Spectral radius preservers of products of nonnegative matrices, Banach J. Math. Anal. 2 (2008), 107-120.
  • A. Isgur** and I. Spitkovsky, On the spectra of some Toeplitz and Wiener-Hopf operators with almost periodic matrix symbols, Operators and Matrices 2 (2008), 371--383.
  • S. Clark**, C.K. Li  and A. Rastogi**, Schur multiplicataive maps on matrices, Bulletin of Aust. Math. Soc. 77 (2008), 49-72.
  • B. Hoai*, C.R. Johnson, and I. Spitkovsky, Spectral dominance and commuting chains. Proceedings of the AMS 136 (2008), 2019--2029.
  • D. Rose** and I. Spitkovsky, On the the stabilization of the Aluthge sequence, International Journal of Information and System Sciences, 4 (2008), 178--189.
  • D. Rose** and I. Spitkovsky, On the numerical range behavior under the generalizedi Aluthge transform, Linear and Multilinear Algebra, 56 (2008), 163--177.
  • C.K. Li , E. Poon  and A. Rastogi**, Maps preserving spectral radius, numerical radius, spectral norm, Electronic Linear Algebra 16 (2007), 347-359.
  • S.J. Schreiber, and M. Vejdani.** Handling time promotes the coevolution of aggregation in predator-prey systems. Proceedings of the Royal Society: Biological Sciences. 273, (2006), 185-191.
  • M. Alwill*, C.K. Li , C. Maher*, N.S. Sze, Automorphisms of certain groups and semigroups of matrices, Linear Algebra Appl. 412 (2006), 490-525.
  • M. Holroyd** and R. Kincaid,  Synchronizability and connectivity of discrete complex systems,  in Proccedings of the International Con$ on Complex Systems 2006, New England Complex Systems Institute, Quincy, MA. June (2006).
  • Y. H. Lee**, L. Sherbakov**, J. Taber** and J. Shi,  Bifurcation Diagrams of Population Models with Nonlinear Diffusion.  Journal of Computational and Applied Mathematics, 194(2), (2006), 357-367.
  • Funk, W**. and Lutzer, D., Branch space represetnations of lines, Topology and its Applications, 151(2005), 187-214.
  • Funk, W**. and Lutzer, D., Lexicographically ordered trees, Topology and its  Applications, 152(2005), 275-300.
  • Keagy**, J., S.J. Schreiber, and D. A. Cristol, Replacing sources with sinks: When do populations begin to go down the drain? Restoration Ecology 13, (2005), 529-535.
  • S.J. Schreiber, and M. Kelton**, Sink habitats alter ecological outcomes of competing species. Journal of Animal Ecology. 74, (2005), 995-1004
  • Rugierri**, E. and S.J. Schreiber, Dynamics of the Schoener-Holt model of intraguild predation. Mathematical Biosciences and Engineering. 2, (2005) 279–288.
  • H. Chiang** and C.K. Li, Generalized Doubly Stochastic Matrices and Linear Preservers, Linear and Multilinear Algebra 53 (2005), 1-11.
  • R. Brualdi, H. Chiang** and C.K. Li, A Partition Problem for Sets of Permutation Matrices, Bulletin of ICA 43 (2005), 67-79.
  • C.R. Johnson, S. Leichenauer*, P. McNamara*, and R. Costas, Principal minor sums of $(A+tB)^m$, Linear Algebra and Appl. 411(2005), 386-389.
  • C. Hillar* and C.R. Johnson, On the postitivity of the coefficients of a certain polynomial defined by two positive definite matrices, J. Stat. Physics 118(2005), 781-789.
  • C.R. Johnson, R. Masson*, and M. Trosset, On the diagonal scaling of Euclidean distance matrices to doubly stochastic matrices, Linear Algebra and Appl. 397(2005), 253-264.
  • C.R. Johnson and B. Sutton*, Hermitian matrices, eigenvalue multilpicities, and eigenvector components, SIAM J. Matrix Anal. Appl. 26(2004/5), 390-399.
  • E. Brown* and  I. Spitkovsky, On flat portions on the boundary of the numerical range, Linear Algebra and Applications 390 (2004), 75--109.
  • S. J. Schreiber and S. Rittenhouse*, From simple rules to cycling in community assembly, Oikos, 105 (2004) 349-358.
  • V. Bolotnikov and P. A. Smith**, Positive extension problems for a class of structured matrices, Linear Algebra Appl. 381 (2004), 165-195.
  • Frank Curtis**, John Drew, C.K. Li, and Daniel Pragel*, Central Groupoids, Central Digraphs, and Zero-One Matrices $A$ Satisfying $A^2 = J$ J. Combinatorial Theory, Series A, 105 (2004), 35-50.
  • E. Brown* and  I. Spitkovsky, On matrices with elliptical numerical ranges. Linear and Multilinear Algebra 132 (2004), no. 4, 945--953.
  • C. Hillar* and C.R. Johnson, Symmetric word equations in two positive definite letters. Accepted by Proc. Amer. Math. Soc. 132 (2004), no. 4, 945--953.
  • H. Chiang** and C.K. Li,  Linear Maps Leaving Invariant Subsets of Nonnegative Symmetric Matrices. Bulletin of Australian Math. Soc. 68 (2003), 221-231.
  • Liz Dolan**, Michael Lewis, and Virginia Torczon, On the local convergence of pattern search. SIAM Journal on Optimization 14 (2003), no. 2, 567--583.
  • S.M. Henson, J. R. Reilly**, S. L. Robertson**, M. C. Schu**, E. W. Davis**, and J. M. Cushing, Predicting Irregularities in Population Cycles. SIAM J. Applied Dynamical Systems, 2, (2003), no.2, 238--253.
  • S. J. Schreiber and G. A. Tobiason*, The evolution of resource use. Journal of Mathematical Biology, 47, (2003), no. 1, 56--78.
  • N. McCarthy*, D. Ogilvie*,  V. Zobin, and N. Zobin, Convex geometry of Coxeter-invariant polytopes,  Contemp. Math. 321, (2003), 153--180.
  • C.R. Johnson, A. Leal-Duarte, C. Saiago, B. Sutton*, and W. Witt*, On the relative position of multiple eigenvalues in the spectrum of an Hermitian matrix with a given graph. Linear Algebra Appl. 363 (2003), 147--159.
  • C.R. Johnson and C. Hillar*, Eigenvalues of words in two positive definite letter. SIAM J. Matrix Analysis Appl. 23 (2002), no. 4, 916--928.
  • S.W. Malone*, P. Tarazaga, and M.W. Trosset, Better initial configurations for metric multidimensional scaling. Computational Statistics and Data Analysis, 41, (2002), 143--156.
  • J. W. McLean** and H. J. Woerdeman, Spectral factorizations and sums of squares representations via semidefinite programming.  SIAM J. Matrix Anal. Appl. 23 (2001/02), no. 3, 646--655.
  • V. Bolotnikov, C.K. Li, P. Meade**, C. Mehl, and L. Rodman, Shells of matrices in indefinite inner product spaces. Electron. J. Linear Algebra 9 (2002), 67--92.
  • J. Brandman*, J. Fowler*, B. Lins**, I. Spitkovsky, and N. Zobin, Convex hulls of Coxeter groups, in "Proceedings of the Conference on Function Spaces and Interpolation of Operators", Walter de Gruyter, Berlin-New York, 2002, 213--240.
  • N. McCarthy*, D. Ogilvie*, I. Spitkovsky, and N. Zobin, Birkoff's Theorem and convex hulls of Coxeter groups, Linear Algebra Appl. 347 (2002), 219--231.
  • C. Hillar*, C.R. Johnson, and I. Spitkovsky, Positive eigenvalues and two-letter generalized words, Electronic Journal of Linear Algebra 9 (2002), 21-26.
  • H. Chiang** and C.K. Li, Linear maps leaving the alternating group invariant, Linear Algebra Appl. 340 (2002), 69-80.
  • L. Caston*, M. Savova*,  I. Spitkovsky, and N. Zobin, On eigenvalues and boundary curvature of the numerical range, Linear Algebra and Applications, 322, no. 1-3, (2001), 129--140.
  • B. Lins**, P. Meade**, C. Mehl, and L. Rodman, Normal Matrices and Polar Decompositions in Indefinite Inner Products, Linear and Multilinear Algebra 49 (2001), no. 1, 45--89.
  • A. Crans*, S. Fallat, and C.R. Johnson, The Hadamard Core of the totally nonnegative matrices, Linear Algebra Appl. 328 (2001), 203-222.
  • J. Drew, C. R. Johnson, and Fumei Lam*, Complete a positivity of matrices of special form, Linear Algebra and Applications 327 (2001), 121-130.
  • C.R. Johnson, S. Lewis*, and D. Yau*, Sign patterns that allow given line sums, Linear Algebra and Applications 327 (2001), 53--60.
  • A. A. Bostian** and H. J. Woerdeman, Uniticity of minimal rank completions for tri-diagonal partial block matrices, Linear Algebra and its Applications 325 (2001), 23-55.
  • L. Caston*, M. Savova*, I. Spitkovsky, and N. Zobin, On eigenvalues and boundary curvature of the numerical range, Linear Algebra and its Applications 322 (2001), 129--140.
  • C.K. Li and S. Nataraj**, Some matrix techniques in game theory, Mathematical Inequalities and Applications 3 (2000), 133-141.
  • Adam L. Cohen*, L. Rodman, and David P. Stanford, Pointwise and Uniformly Convergent Sets of Matrices, SIAM J. Matrix Anal. Appl. 21 (1999). no. 1, 93--105. [Erratum in SIAM J. Matrix Anal. Appl. 22 (2000), no. 3, 971.]
  • J. H. Drew, C.R. Johnson, S. J. Kilner*, and A. M. McKay*, The cycle completable graphs for the completely positive and doubly nonnegative completion problems, Linear Algebra Appl. 313 (2000), no. 1-3, 141--154.
  • C.R. Johnson, Joel Pitkin*, and David P. Stanford, Line-sum Symmetry via the DomEig Algorithm, Computational Optimization and Applications 17 (2000), 5--10.
  • B. Arkin** and L. Leemis, Nonparametric Estimation of the Cumulative Intensity Function for a Nonhomogeneous Poisson Process from Overlapping Intervals, Management Science 46 (2000), no. 7, 989-998.
  • I. Spitkovsky and D. Yong*, Almost periodic factorization of certain block triangular matrix functions, Mathematics of Computation 69 (2000), no. 231, 1053-1070.
  • C.K. Li, J. Lin*, and L. Rodman, Determinants of certain classes of zero-one matrices with equal line sums, Rocky Mountain J. 29 (1999), 1363-1385.
  • G. S. Cheon, S. G. Lee, C.R. Johnson, and E. Pribble*, The possible number of zeros in an orthogonal matrix, Elec. J. Lin. Alg. 5 (1999), 19-23.
  • Yu. Karlovich, I. Spitkovsky, and R. Walker*, Almost periodic factorization of block triangular matrix functions revisited, Linear Algebra and Applications 293 (1999), 199-232.
  • C.K. Li and I. Nelson**, Perfect Codes on the Towers of Hanoi Graph, to appear in Bulletin of the Australian Math. Soc. 57 (1998), no. 3, 367-376.
  • S. Fallat, H. T. Hall*, and C.R. Johnson, Chracterization of product inequalities for principal minors of M- and inverse M-matrices, Q.J. Math. (Oxford) 49:2 (1998), 451-458.
  • C.K. Li and C. Pohanka**, Estimating the Extreme Singular Values of Matrices, Mathematical Inequalities and Applications 1 (1998), 153-169
  • D. Quint*, L. Rodman, and I. Spitkovsky, New cases of almost periodic factorization of triangular matrix functions, Michigan Math. J. 45 (1998), 73-102.
  • M. Gelfand* and I. Spitkovsky, Almost periodic factorization: Applicability of the division algorithm, Advances in Mathematical Sciences 184 (1998), 97-109.
  • T. Coleman*, C.K. Li, M. Lundquist, and T. Travison*, Isometries for the induced c-norm on square matrices and some related results, Linear Algebra Appl. Linear Algebra Appl. 271 (1997), 235-256.
  • C.K. Li, S. Shukla*, and I. Spitkovsky, Equality of higher numerical ranges of matrices and a conjecture of Kippenhahn on Hermitian pencils, Linear Algebra Appl. Linear Algebra Appl. 270 (1997), 323-349.
  • D. Keeler*, L. Rodman, and I. Spitkovsky, The Numerical Range of 3-by-3 Matrices, Linear Algebra and Applications 252 (1997), 115-139.
  • C.R. Johnson and J. S. Miller*, Rank Decomposition under Combinatorial Constraints, Linear Algebra and its Applications 251 (1997), 97-104.
  • C. Cates*, J. H. Drew, C.R. Johnson, and J. H. Tart*, Characterization of Supercommuting Matrices, Linear and Multilinear Algebra 43 (1997), 35-51.
  • G. Hartless* and L. Leemis, Computational Algebra Applications in Reliability, IEEE Transactions on Reliability 45 (1996), 393-399.
  • J. Karro** and C.K. Li, A unified elementary approach to matrix cannonical form theorems, SIAM Review 39 (1997), 305-309.
  • B. I. Wainberg* and H. J. Woerdeman, The Maximum Row Sum Nonsingularity Radius, Linear Algebra Appl., 247 (1996), 251-264.
  • C. Hamilton-Jester* and C.K. Li, Extreme vectors of doubly nonnegative matrices, Rocky Mountain J. of Math. 26 (1996), 1371-1383.
  • C.K. Li  and W. Whitney*, Symmetric overgroups of S_n in O_n Canad. Math. Bulletin 9 (1996), 83-94.
  • A-L. Klaus** and C.K. Li, Isometries for the Vector (p,q) and Induced (p,q) Norms, Linear and Multilinear Algebra 38 (1995), 315-332.
  • C.R. Johnson, C. A. Jones*, and B. Kroschel, The Euclidean Distance Completion Problem: Cycle Completability, Linear and Multilinear Algebra 39 (1995), 195-207.
  • C.K. Li and P. Mehta*, Permutation Invariant Norms, Linear Algebra and its Applications 219 (1995), 93-110.
  • J. Hinkley, R. Kincaid, and A. Martin**, Heuristic Search for the Polymer Straightening Problem,'' Computational Polymer Science, 5 (1995) pp. 1-5.
  • R. Kincaid, W. Mao, and A. Rifkin**, On-Line Scheduling Algorithms, The Impact of Emerging Technologies on Computer Science and Operations Research, A. Sofer and S. Nash (editors) (1995) pp. 157-171.
  • R.T. Berger** and R. Kincaid, The Maxminsum Problem on Trees, Location Science, 2 (1994) pp. 1-10.
  • D. P. Stanford and J. Urbano*, Some Convergence Properties of Matrix Sets, SIAM J. on Matrix Analysis and Applications 15 (1994), 1132-1140.
  • C.R. Johnson,  D. Olesky, P. vanden Driessche, and D. Hare*, Sparsity analysis of the QR factorization, SIAM J. Matrix Anal. Appl 14 (1993), 655-669.
  • S. Gottlieb*, C. R. Johnson, and I. Spitkovsky,  Inequalities Involving the Numerical Radius, Linear and Multilinear Algebra, 37 (1994), 13-24.
  • J.W. Helton, D. Lam*, and H. J. Woerdeman, Sparsity Patterns with High Rank Extremal Semipositive Definite Matrices, SIAM J. Matrix Anal. Appl. 15 (1994), 299-312.
  • C.K. Li, P. Mehta*, and L. Rodman, Linear Operators Preserving the Inner and Outer c-spectral Radii, Linear and Multilinear Algebra 36 (1994), 195-204.
  • C.K. Li, P. Mehta*, and L. Rodman, A Generalized Numerical Range: the Range of a Constrained Sesquilinear Form, Linear and Multilinear Algebra 34 (1994), 25-49.
  • C.R. Johnson  and C. Xenophontos**, Irreducibility and primitivity of Perron complements: application of the compressed directed graph, In "Graph theory and sparse matrix computation", Vol. Math. Appl., 56, Springer, New York, 1993, pp. 101-106.
  • C.R. Johnson, K. Kerr*, and D. Stanford, Semipositivity of matrices, Linear and Multilinear Algebra 37 (1994), 265-271.
  • R.T. Berger** and R. Kincaid, The Damper Placement Problem on Space Truss Structures, Location Science 1 (1993) pp. 219-234.
  • R. Kincaid and L.G. Yellin**, The P-Dispersion-Sum Problem: Results on Trees and Graphs, Location Science, 1 (1993) pp. 171-186.
  • A. C. M. Ran, L. Rodman, and J. E. Rubin**, Direct Complements of Invariant Lagrangian Subspaces and Minimal Factorization of Skew-symmetric Rational Matrix Functions. Linear Algebra and its Applications 180 (1993), 61-94.
  • S. Chang* and C.K. Li, Certain Isometries on R^n, Linear Algebra and Applications 165 (1992), 251-261.
  • S. Chang* and C.K. Li, A special linear operator on M_4(R), Linear and Multilinear Algebra 30 (1991), 65-75
  • C.R. Johnson and G. Whitney*, Minimal Rank Completions, Linear and Multilinear Algebra 28 (1991), 271-273.
  • C.R. Johnson, F. Leighton*, and H. Robinson, Sign patterns of inverse positive matrices, Linear Algebra Appl. 24 (1979), 75-83.
  • C.R. Johnson and F. Leighton*, An efficient liner algebraic algorithm for the determination of isomorphism in pairs of undirected graphs, J. Research of the National Bureau of Standards 80B (1976), 447-483.