**Preprints**

**Published Articles**

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.

69. Bounds and extremal domains for Robin eigenvalues with negative boundary parameter

*Adv. Calc. Var. *
** 10 ** (2017), 357-379
(with
Pedro R.S. Antunes and David Krejčiřík).

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
harmonic oscillator

*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 R^{n}

*
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
hypersurfaces

*
Dokl. Akad. Nauk.* **442** (2012), 151-155;
translation in *
Dokl. Math.* **85** (2012), 18-22
(with Denis Borisov).

49. Sharp estimates and saturation phenomena for a nonlocal
eigenvalue problem

*
Adv. Math.* **228** (2011), 2352-2365
(with Barbara Brandolini,
Carlo Nitsch
and Cristina Trombetti).

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
and quadrilaterals

*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 R^{d}

*
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).

40. Hearing the weights of weighted
projective planes

*Ann.
Global Anal. Geom. * **33** (2008), 373-395 (with Miguel
Abreu, Emily
B. Dryden and Leonor Godinho).

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).

37. A
numerical study of the spectral gap

*J.
Phys. A* **41** (2008), 055201 (with Pedro
R.S. Antunes).

36. On
convex surfaces with minimal moment of inertia

*J. Math. Phys.
***48** (2007), 122902 (with Richard
S. Laugesen and Gerrard
F. Liddell).

35.
Precise bounds and asymptotics for the first Dirichlet eigenvalue of
triangles and rhombi

*J. Funct. Anal.*
**251** (2007), 376-398.

34.
Unbounded planar domains whose second nodal
line does not touch the boundary

*Math.
Res. Lett.* **14** (2007), 107-111 (with David
Krejčiřík).

33.
Waveguides with combined Dirichlet and Robin
boundary conditions

*Math. Phys. Anal.
Geom.* **9** (2006), 335-352 (with David
Krejčiřík).

32.
New bounds for the principal Dirichlet eigenvalue of planar regions

*Experiment. Math. ***15** (2006),
333-342 (with
Pedro
R.S. Antunes).

31. A
Li-type criterion for zero-free half-planes of Riemann's zeta
function

*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.

29. Extension
of Abel's Lemma with q-series implications

*Ramanujan J.* **10** (2005), 137-152 (with George
E. Andrews).

28. Geometrically
induced discrete spectrum in curved tubes

*Differential Geom. Appl.* **23** (2005), 95-105
(with Boris Chenaud, Pierre
Duclos and David
Krejčiřík).

27. Integrals
of polylogarithmic functions, recurrence relations, and associated
Euler sums

*Math. Comp.* **74**
(2005), 1425-1440.

26. Instability
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.

22. Memory
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 S^{1}-invariant
metrics on S^{2}

*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.

19. Lyapunov
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)

2.
The Robin problem

in *
Shape optimization and spectral theory*,
2017, 78-119

Antoine Henrot (ed.), De Gruyter.
(with Dorin Bucur
and James B. Kennedy)

1. *Topics
in functional differential and difference equations
Fields Inst. Commun.*

**
Proceedings
**

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
indefinite damping

*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).

**
Reports
**

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).

11. Modelling fiber flow in fiberboard manufacturing

*86th European Study Group with Industry*
(2012)
(with Diogo Pinheiro,
João Penedones
and José Matos).

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).

7. Fraud detection in plastic card operations

*69th European Study Group with Industry*
(2009)
(with Paulo C.
Aguiar and António J. Rodrigues).

6. Approximating low eigenvalues of the Laplacian:
analysis, geometry and numerics

*Oberwolfach report* no. 06/2009.

5. Scheduling in a factory

*65th European Study Group with Industry*
(2008)
(with Jorge Orestes Cerdeira, Tiago Charters, Manuel Cruz and Paulo Vasconcelos).

4. Electrostatic separation of rubber and textiles

*65th European Study Group with Industry*
(2008).

3. Cooling of a rotor

*65th European Study Group with Industry*
(2008)
(with Nuno Lopes).

2. Stewart platform

*
60th European Study Group with Industry* (2007)
(with Tiago Charters
and Ricardo Enguiça).

1. Sharp *dynamic* bounds for eigenvalues of the
Laplacian

*Oberwolfach report* no. 18/2007.

**
Other
**

2.
European Study Groups with Industry at 40 years

*SIAM News*, March 2009.

1.
European Study Groups with Industry in Portugal:
importing a forty year old concept

* CIM Bulletin*, December 2008.