Publications of Mathematics Faculty with Undergraduates
(Students
in William and Mary's summer 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 William and Mary undergraduate student
- 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.
- Y. H. Lee**, L.
Sherbakov**, J. Taber** and J.
Shi, Bifurcation
Diagrams
of Population Models with Nonlinear Diffusion. Accepted by Journal
of Computational and Applied Mathematics.
- 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.
- 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*, Leiba
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.
- Charles 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 Leiba
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.
Updated by J. Shi, Sept. 10th, 2003