Orthogonal Families of Bicircular Quartics, Quadratic Differentials, and Edwards Normal Forms, Axioms 2023, 12(9), 870; https://doi.org/10.3390/axioms12090870

Confocal Families of Hyperbolic Conics Via Quadratic Differentials, Axioms 2023, 12, 507. https:// doi.org/10.3390/axioms12060507

The Trefoil Soliton,
Mathematics, MDPI, **10** (2022), 1512, doi.org/10.3390/math10091512.

The Trefoil Spline, (with Troy Clark), Computer-Aided Design & Applications, 19(6), 2022, 1255-1269

On the geometric mean of a pair of oriented, meromorphic foliations, Part I, (with Joel Langer) Complex Analysis and its Synergies 4:4(2018), doi.org/10.1186/s40627-018-0015-z.

Secrets of Linear Feedback Shift Registers, Mathematics Magazine, 2021 (to appear in 2022)..

Flat Curves (with Joel Langer), Mediterranean Journal of Mathematics (2017), 14:236.

The
Trefoil, (with Joel Langer), Milan
Journal, **82** (2014),161-182.

Numerical Approximation
of the Field of Values of the Inverse of a Large Matrix (with Michiel
Hochstenback and Paul Zachlin), Textos de Matematica **44** (2013),59-71.

Subdividing the Trefoil by Origami (with Joel Langer), Geometry 1 (2012).

The
Lemniscatic Chessboard, (with Joel Langer), Forum Geometricorum 11 (2011),
183{199.

Reflections
on the lemniscate of Bernoulli: The forty-eight faces of a mathematical
gem, (with Joel Langer), Milan.
J. Math., **78**, Number 2 (2010), 643--682.

When
is a Curve an Octahedron?, (with Joel Langer), American
Mathematical Monthly, **117**, Number 10, December 2010 , pp. 889-902.

Lectures
on Elastic Curves and Rods, Curvature and Variational Modeling in Physics
and Biophysics, Conference Proceedings of the American Institute of Physics,
**1002** (2008), 3-32.

Foci
and Foliations of Algebraic Curves, (with Joel Langer), Milan. Journal of
Mathematics **75** (2007), 225--271.

Eigenvalue inclusion regions from inverses of shifted matrices, (with Michiel E. Hochstenbach and Paul F. Zachlin), Linear Algebra and its Applications 429 (2008), 2481-2496.

The location of critical points of Finite blaschke products, Conform. Geom. Dyn. 10 (2006), 117-124.

Anti-Tamper Databases: Querying Encrypted Databases, 17th Annual IFIP WG 11.3 Working Conference on Database and Applications Security, Estes Park, Colorado, August 4-6, 2003 (with G. Ozsoyoglu and Sun S. Chung).

A New Flow on Starlike Curves in ,
Proc.
Amer. Math. Soc. **130 **(2002), 2725-2735 (with Rongpei
Huang).

Diffeomorphisms of the circle and hyperbolic curvature, Conform. Geom. Dyn. 5 (2001), 1-5.

Curves whose Curvature Depends on
Distance from the Origin, Am. Math. Monthly **106** (1999), 835-841.

Knot Types, Homotopies and Stability
of Closed Elastic Rods, Proceedings of the London Mathematical Society (1999),
**79**:429-450 (with Tom
Ivey).

Elasticae
with Constant Slant in the Complex Projective Plane and New Examples of Willmore
Tori in Five-spheres, (with M. Barros and O. Garay), Tokohu Math Journal
**51** (1999), 177-192.

Lagrangian Aspects of the Kirchhoff Elastic Rod, SIAM Review **38** (1996),
605-618 (with Joel
Langer). (JSTOR
link)

Liouville Integrability of Geometric Variational Problems, Comment.
Math. Helvetici **69** (1994), 272-280 (with Joel Langer).

Isometries of the Plane, Am.
Math. Monthly ** 102** (1994), 628-631.

Normal Forms for Lorentzian Spaces, Nova Journal of Algebra and Geometry **3**
(1994), 1-10 (with Dan Steinberg). Preprint version here.

A new structural framework for parity equation-based failure detection and isolation, Automatica Volume 26, Issue 2 , March 1990, Pages 381-388 (with Janos Gertler).

Curve-straightening
in Riemannian manifolds, (with J. Langer), Ann. Global Anal. Geom. **5**
(1987), 133-150.

Curve straightening and a minimax argument for closed elastic curves.
Topology
**24** (1985), no. 1, 75--88 (with Joel Langer).

Knotted elastic curves in R^3, (with J. Langer),
J. London Math. Soc.(2) **30 **(1984), 512-520.

Curves in the hyperbolic plane and mean curvature of tori in 3-space, (with
J. Langer), Bull.
London Math. Soc.**16** (1984), 531-534.

The
total squared curvature of closed curves, (with J. Langer), J. Diff. Geometry
**20** (1984), 1-22.

Diffeomorphisms of the Circle and Geodesic Fields on Riemannian Surfaces of
Genus One, Invent.
math. **69** (1982), 229-242 (with Joel Langer).

Scattering of geodesic fields. II. Ann.
of Math. (2) **110** (1979), no. 2, 205--225. (see also I)(with
Herman Gluck)

Stable orbits and bifurcation of maps of the interval. SIAM
J. Appl. Math. **35** (1978), no. 2, 260--267.

The
existence of nontriangulable cut loci, (with H. Gluck), Bull. Am. Math.
Soc. **82** (1976), 599-602.

Deformations of
geodesic fields, (with H. Gluck), Bull. Am. Math. Soc.** 82** (1976),
571-574.

The converse to the
Gauss-Bonnet theorem in PL, (with H. Gluck and K. Krigelman), J. Diff. Geometry
**9** (1974), 601-616.

Preassigning curvature on polyhedra homeomorphic to the 2-sphere, J. Diff. Geometry {\bf 9} (1974), 633-638.

Here is an ancient paper of mine, never before published, on Rectilinear Crossing Numbers.

* In some cases, access is restricted.

David Singer

Professor of Mathematics

College of Arts and Sciences

Case Western Reserve University

Cleveland, Ohio 44106-7058 E-mail: das5@case.edu

Phone: (216)368-2892

Fax: (216)368-5163

This page last changed on Sunday**, April 26, 2015**