"Pipes, Trompes, Nakeres, and Clariounes,
That in the Bataille blowen blody sounes."
--Chaucer, The Knight's Tale.

Publications

On Riesz Means of Eigenvalues (with E. M. Harrell, submitted, preprint Dec 2007); also available at arXiv.

Differential inequalities for Riesz means and Weyl-type bounds for eigenvalues (with E. M. Harrell, submitted, preprint May 2007); also available at arXiv.

Two new Weyl-type bounds for the Dirichlet Laplacian, Trans. Amer. Math. Soc. 360 (2008), 1539-1558.

Mini-Workshop: Shape Analysis for Eigenvalues (Oberwolfach Report No. 18/2007, April 8-14, 2007)

A unified approach to universal inequalities for eigenvalues of elliptic operators, (with M. S. Ashbaugh, Pacific Journal of Mathematics, Vol. 217 (2004), pp. 201-220.)

On extending the inequalities of Payne, Polya, and Weinberger using spherical harmonics (with M. S. Ashbaugh, Rocky Mountain Journal of Mathematics, Vol. 38, No. 4, 2008.).

On Harrell-Stubbe type inequalities for the discrete spectrum of a self-adjoint operator (with M. S. Ashbaugh, submitted)

Shape recognition using eigenvalues of the Dirichlet Laplacian, Pattern Recognition, v.40, n.1, p.141-153, January, 2007. (with M. A. Khabou and M. B. H. Rhouma)

Feature generation using the Laplacian operator with Neumann boundary condition, IEEE Proceedings, March 2007, pp. 766-771 SoutheastCon, 2007, Richmond, VA, USA (with M. A. Khabou and M. B. H. Rhouma)

Universal inequalities for higher-order elliptic operators" (with M. S. Ashbaugh, preprint).

On Yang-type bounds for eigenvalues with applications to physical and geometric problems, (with M. S. Ashbaugh, preprint).

On domain-dependent inequalities for the eigenvalues of the Dirichlet-Laplacian, (with M. S. Ashbaugh, preprint).

Bounds for sums of eigenvalues of elliptic operators with application to physical and geometric problems (preprint).

Yang-type inequalities for the eigenvalues of a tree (in preparation).

An asymptotic analysis of the inequalities of Harrell-Stubbe and H. C. Yang (in preparation).