PUBLICATIONS

Journal Articles

• M. S. Ashbaugh, F. Gesztesy, L. Hermi, K. Kirsten, L. Littlejohn, and H. Tossounian, Trace Formulas Applied to the Riemann ζ-Function, In: S. Kuru et al. (eds.), Integrability, Supersymmetry and Coherent States, CRM in Mathematical Physics, pp. 231--253, Springer 2019.
• M. S. Ashbaugh, F. Gesztesy, L. Hermi, K. Kirsten, L. Littlejohn, and H. Tossounian, Green's functions and Euler's formula for ζ(2n). Schrödinger operators, spectral analysis and number theory, 27-45, Springer Proc. Math. Stat., 348, Springer, Cham, [2021]
• L. Hermi, N. Saito, On Rayleigh-type formulas for a non-local boundary value problem associated with an integral operator commuting with the Laplacian, Appl. Comput. Harmon. Anal., Volume 45, Issue 1, July 2018, 59--83.
• A. Hasnaoui, L. Hermi, A sharp upper bound for the first Dirichlet eigenvalue of a class of wedge-like domains. Z. Angew. Math. Phys. (ZAMP), 2015, DOI 10.1007/s00033-015-0530-1.
• A. Hasnaoui, L. Hermi, Isoperimetric inequalities for a wedge-like membrane. Ann. Henri Poincaré 15 (2014), no. 2, 369--406.
• E. M. Harrell, L. Hermi, On Riesz means of eigenvalues. Comm. Partial Differential Equations 36 (2011), no. 9, 1521--1543.
• W. M. Greenlee, L. Hermi, Quadratic interpolation and Rayleigh-Ritz methods for bifurcation coefficients. SIAM J. Math. Anal. 42 (2010), no. 6, 2987--3019.
• M. S. Ashbaugh, L. Hermi, On extending the inequalities of Payne, Polya, and Weinberger using spherical harmonics. Rocky Mountain J. Math. 38 (2008), no. 4, 1037--1072.
• E. M. Harrell, L. Hermi, Differential inequalities for Riesz means and Weyl-type bounds for eigenvalues. J. Funct. Anal. 254 (2008), no. 12, 3173--3191.
• L. Hermi, Two new Weyl-type bounds for the Dirichlet Laplacian. Trans. Amer. Math. Soc. 360 (2008), no. 3, 1539--1558.
• M. Khabou, L. Hermi, M.B.H. Rhouma, Shape recognition using eigenvalues of the Dirichlet Laplacian. Pattern Recognition Journal 40(2007), 141--153.
• M. S. Ashbaugh, L. Hermi, A unified approach to universal inequalities for eigenvalues of elliptic operators. Pacific J. Math. 217 (2004), no. 2, 201--219.

Invited Book Chapters (Peer Reviewed)

• M.A. Khabou, M.B.H. Rhouma, L. Hermi, Shape Recognition Based on Eigenvalues of the Laplacian. In: Peter W. Hawkes, editor, Advances in Imaging and Electron Physics, Vol 167, pp. 185--254, Academic Press, San Diego, 2011.
• N. Gamara, A. Hasnaoui, L. Hermi, Max-to-mean ratio estimates for the fundamental eigenfunction of the Dirichlet Laplacian. Entropy and the quantum II, Robert Sims and Daniel Ueltschi, eds., 61--70, Contemp. Math., 552, Amer. Math. Soc., Providence, RI, 2011.

Proceedings

• E. M. Harrell, L. Hermi, A class of new inequalities for the eigenvalues of the Dirichlet Laplacian, Oberwolfach Reports, Report # 06/2009.
• E. M. Harrell, L. Hermi, On Riesz and Carleman Means of Eigenvalues, Oberwolfach Reports, Report # 18/2007.
• M.A. Khabou, M.B.H. Rhouma, L. Hermi, Laplacian and Bilaplacian Based Features for Shape Classification, Proc. Int'l Conference on Image Processing, Computer Vision, and Pattern Recognition, Las Vegas, NV (2009).
• M.A. Khabou, M.B.H. Rhouma, L. Hermi, Feature generation using the Laplacian operator with Neumann boundary condition, IEEE Proceedings, March 2007, pp. 766-771 SoutheastCon, 2007, Richmond, VA, USA.

Work in Progress

• L. Hermi, N. Saito, On a Nonlocal Integral Operator Commuting with the Laplacian and the Sturm-Liouville Problem I: Low Rank Perturbations of the Operator (Preprint, Nov 14, 2022, submitted)
• A. Hasnaoui, L. Hermi, Isoperimetric inequalities for convex cones, submitted.
• A. Hasnaoui, L. Hermi, Isoperimetric inequalities for relative torsional rigidity of a wedge-like membrane, submitted.
• M. S. Ashbaugh, L. Hermi, On Harrell-Stubbe type inequalities for the discrete spectrum of a self-adjoint operator, 42 pp.
• M. S. Ashbaugh, L. Hermi, Universal inequalities for higher-order elliptic operators, preprint 2004.
• L. Hermi, D. Hughes Hallett, W. C. McCallum, A Mathematical Exploration of Apportionment Procedures Around the World (2004). Excel files updated 2013.

Conferences Organized

• From Carthage to the World: The Isoperimetric Problem of Queen Dido and its Mathematical Ramifications, Carthage, Tunisia, 24-29 May, 2010
• The Learning Technologies and Mathematics Middle East Conference, Sultan Qaboos University, Muscat, Oman, March 31-April 2, 2007

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