A remark on Pólya's conjecture at low frequencies
Arch. Math. (Basel)
The spectral determinant of the isotropic quantum harmonic oscillator in arbitrary dimensions
Math. Ann. 372 (2018), 1081–1101
The spectral determinant of the isotropic quantum harmonic oscillator in arbitrary dimensions
72. The damped wave equation with unbounded damping
J. DIfferential Eq. 264 (2018), 7023-7054 (with Petr Siegl and C. Tretter).
71. Decay of solutions for a class of nonlinear Schrödinger equations in R and the stability of shock profiles for a quasilinear Benney system
Nonlinearity 31 (2018), 1110-1119 (with João-Paulo Dias).
70. Sharp bounds for the modulus and phase of
Hankel functions with applications to Jaeger integrals
Math. Comp. 87 (2018), 289-308.
68. The spectrum of geodesic balls on spherically symmetric manifolds
Comm. Anal. Geom. 25 (2017), 507-544 (with Denis Borisov).
67. Eigenvalue asymptotics for the damped wave equation on metric graphs
J. Differential Eq. 263 (2017), 2780-2811 (with Jiří Lipovský).
66. Asymptotic behaviour of extremal averages of Laplacian eigenvalues
J. Stat. Phys. 167 (2017), 1511-1518.
65. Summation formula inequalities for eigenvalues of Schrödinger operators
J. Spectral Theory 6 (2016), 483-503 (with James B. Kennedy).
64. Optimisation of eigenvalues of the Dirichlet Laplacian with a surface area restriction
Appl. Math. Optimiz. 73 (2016), 313-328 (with Pedro R.S. Antunes).
63. Summation formula inequalities for eigenvalues of the perturbed
Osaka J. Math. 53 (2016), 397-416 (with James B. Kennedy).
62. Alexandrov's isodiametric conjecture and the cut
locus of a surface
Tohoku Math. J. 67 (2015), 405-417 (with David Krejčiřík).
61. The first Robin eigenvalue with negative boundary parameter
Adv. Math. 280 (2015), 322-339 (with David Krejčiřík).
60. Spectra of graphene nanoribbons with armchair and zigzag boundary conditions
Rev. Math. Phys. 26 (2014), 1450018 (32 pages) (with Petr Siegl).
59. Optimal ball placement in rugby conversions
SIAM Rev. 56 (2014), 673-690.
58. Spherical symmetrization and the first eigenvalue of geodesic
disks on manifolds
Calc. Var. Partial Differential Equations 51 (2014), 701-724 (with Jing Mao and Isabel Salavessa ).
57. On the spectrum of deformations of compact double-sided flat hypersurfaces
Anal. PDE 6 (2013), 1051-1088 (with Denis Borisov).
56. Asymptotic behaviour of optimal spectral planar domains with fixed perimeter
J. Math. Phys. 54 (2013), 053504 (with Dorin Bucur).
55. Asymptotic behaviour and
numerical approximation of optimal eigenvalues of the Robin Laplacian
ESAIM: Control, Optimisation and Calculus of Variations 19 (2013), 438-459 (with Pedro R.S. Antunes and James B. Kennedy).
54. Asymptotics for the expected lifetime of Brownian motion on
thin domains in Rn
J. Theoret. Probab. 26 (2013), 284-309 (with Denis Borisov).
53. Optimal spectral rectangles and lattice ellipses
Proc. Royal Soc. A Math. Phys. Eng. Sci. 469 (2013), 20120492 (with Pedro R.S. Antunes).
52. On the role of spectral markers
and stability in spine models
J. Mech. Behavior Biomed. Materials 14 (2012), 19-28 (with Pedro R.S. Antunes).
51. Numerical optimization of
low eigenvalues of the Dirichlet and Neumann Laplacians
J. Opt. Theory Appl. 154 (2012), 235-257 (with Pedro R.S. Antunes).
50. Eigenvalue asymptotics for almost flat compact
Dokl. Akad. Nauk. 442 (2012), 151-155; translation in Dokl. Math. 85 (2012), 18-22 (with Denis Borisov).
48. On the inverse
spectral problem for Euclidean triangles
Proc. Royal Soc. A Math. Phys. Eng. Sci. 467 (2011), 1546-1562 (with Pedro R.S. Antunes).
47. A spectral Bernstein theorem
Ann. Mat. Pura Appl. 190 (2011), 77-90 (with Isabel Salavessa ).
46. Bounds for the first Dirichlet eigenvalue of triangles
ESAIM: Control, Optimisation and Calculus of Variations 16 (2010), 646-676 (with Bartlomjej Siudeja).
45. On the characterization of harmonic and subharmonic
functions via mean-value properties
Potential Anal. 32 (2010), 189-200 (with João Palhoto Matos).
44. Asymptotics of Dirichlet eigenvalues and eigenfunctions
of the Laplacian on thin domains in Rd
J. Funct. Anal. 258 (2010), 893-912 (with Denis Borisov).
43. On the effect of sharp rises in blood pressure in the
Shah-Humphrey model for intracranial saccular aneurysms
Biomech. Model. Mechanobiology 8 (2009), 457-471.
42. Eigenvalue asymptotics, inverse problems and a trace
formula for the linear damped wave equation
J. Differential Equations 247 (2009), 3028-3039 (with Denis Borisov).
41. Singular asymptotic expansions
for Dirichlet eigenvalues and eigenfunctions on thin planar domains
Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), 547-560 (with Denis Borisov).
39. A sharp upper bound for the
first Dirichlet eigenvalue and the growth of the isoperimetric
constant of convex domains
Proc. Amer. Math. Soc. 136 (2008), 2997-3006 (with David Krejčiřík).
38. Location of the nodal set for
thin curved tubes
Indiana Univ. Math. J. 57 (2008), 343-376 (with David Krejčiřík).
numerical study of the spectral gap
J. Phys. A 41 (2008), 055201 (with Pedro R.S. Antunes).
convex surfaces with minimal moment of inertia
J. Math. Phys. 48 (2007), 122902 (with Richard S. Laugesen and Gerrard F. Liddell).
Precise bounds and asymptotics for the first Dirichlet eigenvalue of
triangles and rhombi
J. Funct. Anal. 251 (2007), 376-398.
Unbounded planar domains whose second nodal
line does not touch the boundary
Math. Res. Lett. 14 (2007), 107-111 (with David Krejčiřík).
Waveguides with combined Dirichlet and Robin
Math. Phys. Anal. Geom. 9 (2006), 335-352 (with David Krejčiřík).
New bounds for the principal Dirichlet eigenvalue of planar regions
Experiment. Math. 15 (2006), 333-342 (with Pedro R.S. Antunes).
Li-type criterion for zero-free half-planes of Riemann's zeta
J. London Math. Soc. 73 (2006), 399-414.
30. Upper and
lower bounds for the first Dirichlet eigenvalue of a triangle
Proc. Amer. Math. Soc. 134 (2006), 2083-2089.
of Abel's Lemma with q-series implications
Ramanujan J. 10 (2005), 137-152 (with George E. Andrews).
of polylogarithmic functions, recurrence relations, and associated
Math. Comp. 74 (2005), 1425-1440.
results for the damped wave equation in unbounded domains
J. Differential Equations 211 (2005), 168-186 (with David Krejčiřík).
25. On the first twisted Dirichlet eigenvalue
Comm. Anal. Geom. 12 (2004), 1083-1103 (with Antoine Henrot).
24. A lower
bound to the spectral threshold in curved tubes
R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. 460 (2004), 3457-3467 (with Pavel Exner and David Krejčiřík).
23. Closed nodal lines and interior hot spots of the second eigenfunction of the Laplacian on surfaces
Indiana Univ. Math. J. 51 (2002), 305-316.
driven instability in a diffusion process
SIAM J. Math. Anal. 33 (2002), 1090-1106 (with Brian R. Duffy and Michael Grinfeld).
21. On the
invariant spectrum of S1-invariant
metrics on S2
Proc. London Math. Soc. 84 (2002), 213-230 (with Miguel Abreu).
20. On minimal eigenvalues of Schrödinger operators on manifolds
Commun. Math. Phys. 217 (2001), 375-382.
functionals and stability for FitzHugh-Nagumo systems
J. Differential Equations 169 (2001), 208-227 (with Carlos Rocha).
18. Delay induced instabilities in gyroscopic systems
SIAM J. Control Optimization 39 (2000), 196-207.
17. Stability of stationary solutions of nonlocal reaction-diffusion equations in n-dimensional space
Differential and Integral Equations 13 (2000), 265-288 (with Mikhail Vishnevskii).
16. Spectral sequences for quadratic pencils and the inverse spectral problem for the damped wave equation
J. Math. Pures Appl. 78 (1999), 965-980.
15. On the optimal value of the spectral abscissa for a system of linear oscillators
SIAM J. Matrix Anal. Appl. 21 (1999), 195-208 (with Peter Lancaster).
14. Optimizing the rate of decay of solutions of the wave equation using genetic algorithms: a counterexample to the constant damping conjecture
SIAM J. Control Optimization 37 (1999), 376-387.
13. Quadratic matrix polynomials with Hamiltonian spectrum and oscillatory damped systems
Z. Angew. Math. Phys. 50 (1999), 64-81.
12. Nonlocal reaction-diffusion equations
Differential Equations with Applications to Biology 187-204, Fields Inst. Commun. 21, Am. Math. Soc. 1999.
11. Positivity results for a nonlocal elliptic equation
Proc. Roy. Soc. Edinburgh 128 (1998), 697-715 (with Guido Sweers).
10. The linear wave equation, Hamiltonian symmetry, and the importance of being odd
Disc. Cont. Dyn. Syst. 4 (1998), 635-640.
9. Eigenvalue problems for the wave equation with strong damping
Proc. Roy. Soc. Edinburgh A 127 (1997), 755-771.
8. Stability of finite-dimensional systems with indefinite damping
Adv. Math. Sci. Appl. 7 (1997), 435-446 (with Michael Grinfeld and Philip Knight).
7. Some results on the stability and bifurcation of stationary solutions of delay-diffusion equations
J. Math. Anal. Appl. 206 (1997), 59-82.
6. Stability results for the wave equation with indefinite damping
J. Differential Equations 132 (1996), 338-352 (with Enrique Zuazua).
5. On some eigenvalue problems related to the wave equation with indefinite damping
J. Differential Equations 127 (1996), 320-335.
4. Stability of stationary solutions of a nonlocal reaction-diffusion equation
Quart. J. Mech. Appl. Math. 48 (1995), 557-582.
3. Stationary solutions of an equation modelling ohmic heating
Appl. Math. Lett. 7 (1994), 1-6 (with Michael Grinfeld).
2. Bifurcation and stability of stationary solutions of nonlocal scalar reaction-diffusion equations
J. Dynam. Differential Equations 6 (1994), 613-629.
1. A nonlocal Sturm-Liouville eigenvalue problem
Proc. Roy. Soc. Edinburgh A 124 (1994), 169-188.
Books (as editor, book chapters)
in functional differential and difference equations
Fields Inst. Commun. 29, Amer. Math. Soc., Providence, RI, 2001 (co-editor: Teresa Faria).
4. A lower bound to the spectral threshold
in curved quantum layers
Functional Analysis and Operator Theory for Quantum Physics (2017), 261-269
Volume dedicated to Pavel Exner on the occasion of his 70th birthday
J. Dittrich, H.Kovarik, and A. Laptev (eds.), EMS Publishing House (with David Krejčiřík).
3. Characterization and parameterization of the singular
manifold of a simple 6–6 Stewart platform
Nonlinear Science and Complexity (2011), 255-262, J.A.T. Machado et al. eds. (with Tiago Charters).
2. (In)stability results for the wave equation with
Proceedings of Equadiff 95 (1998), 350-355
1. Bogdanov singularity in the FitzHugh-Nagumo equations
Proceedings of Equadiff 91 (1993), 496-500 (with Carlos Rocha).
12. Modelling percolation and fractal structure in aerogels
92nd European Study Group with Industry (2013) (with Adérito Araújo, Joaquim Correia, Michael Grinfeld, Jevgenija Pavlova and Diogo Pinheiro).
10. Asymptotic behaviour of some eigenvalue optimisation problems
Oberwolfach report no. 33/2012.
9. Balanced Scorecard
81st European Study Group with Industry (2011) (with Elisete Correia and Irene Oliveira).
8. Detecting singularities of Stewart platforms
Mathematics-in-Industry Case Studies 1 (2009), 66-80 Fields Institute Publications (with Tiago Charters and Ricardo Enguiça).
6. Approximating low eigenvalues of the Laplacian:
analysis, geometry and numerics
Oberwolfach report no. 06/2009.
4. Electrostatic separation of rubber and textiles
65th European Study Group with Industry (2008).
1. Sharp dynamic bounds for eigenvalues of the
Oberwolfach report no. 18/2007.
European Study Groups with Industry at 40 years
SIAM News, March 2009.
European Study Groups with Industry in Portugal:
importing a forty year old concept
CIM Bulletin, December 2008.