Results 21 to 30 of about 203 (65)
Hearing the shape of a triangle
, 2013 In 1966 Mark Kac asked the famous question 'Can one hear the shape of a drum?'. While this was later shown to be false in general, it was proved by C. Durso that one can hear the shape of a triangle.
Grieser, Daniel, Maronna, Svenja
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Reaction-diffusion problems on time-dependent Riemannian manifolds: stability of periodic solutions
, 2017 We investigate the stability of time-periodic solutions of semilinear parabolic problems with Neumann boundary conditions. Such problems are posed on compact submanifolds evolving periodically in time.
Bandle, Catherine +2 more
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Uniqueness and stability results for an inverse spectral problem in a periodic waveguide [PDF]
, 2015 Let $\Omega =\omega\times\mathbb R$ where $\omega\subset \mathbb R^2$ be a bounded domain, and $V : \Omega \to\mathbb R$ a bounded potential which is $2\pi$-periodic in the variable $x_{3}\in \mathbb R$.
Kavian, Otared +2 more
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The asymptotic limits of zero modes of massless Dirac operators
, 2007 Asymptotic behaviors of zero modes of the massless Dirac operator $H=\alpha\cdot D + Q(x)$ are discussed, where $\alpha= (\alpha_1, \alpha_2, \alpha_3)$ is the triple of $4 \times 4$ Dirac matrices, $ D=\frac{1}{i} \nabla_x$, and $Q(x)=\big(q_{jk} (x) \
A.A. Balinsky +13 more
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On occurrence of spectral edges for periodic operators inside the Brillouin zone [PDF]
, 2007 The article discusses the following frequently arising question on the spectral structure of periodic operators of mathematical physics (e.g., Schroedinger, Maxwell, waveguide operators, etc.). Is it true that one can obtain the correct spectrum by using
+44 more
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, 2006 Estimates are obtained for the expected volume of intersection of independent Wiener sausages in Euclidean space in the small time limit. The asymptotic behaviour of the weighted diagonal heat kernel norm on compact Riemannian manifolds with smooth ...
Berg, M. van den, Gilkey, P.
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On the torsion function with Robin or Dirichlet boundary conditions
, 2013 For $p\in (1,+\infty)$ and $b \in (0, +\infty]$ the $p$-torsion function with Robin boundary conditions associated to an arbitrary open set $\Om \subset \R^m$ satisfies formally the equation $-\Delta_p =1$ in $\Om$ and $|\nabla u|^{p-2} \frac{\partial u}{
Berg, M. van den, Bucur, D.
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On Courant's nodal domain property for linear combinations of eigenfunctions, Part I [PDF]
, 2018 According to Courant's theorem, an eigenfunction as\-sociated with the $n$-th eigenvalue $\lambda\_n$ has at most $n$ nodal domains. A footnote in the book of Courant and Hilbert, states that the same assertion is true for any linear combination of ...
Bérard, Pierre, Helffer, Bernard
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From Quantum $A_N$ to $E_8$ Trigonometric Model: Space-of-Orbits View
, 2013 A number of affine-Weyl-invariant integrable and exactly-solvable quantum models with trigonometric potentials is considered in the space of invariants (the space of orbits).
Turbiner, Alexander V.
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On the number of nodal domains of the 2D isotropic quantum harmonic oscillator -- an extension of results of A. Stern -- [PDF]
, 2014 In the case of the sphere and the square, Antonie Stern (1925) claimed in her PhD thesis the existence of an infinite sequence of eigenvalues whose corresponding eigenspaces contain an eigenfunction with two nodal domains. These two statements were given
Bérard, Pierre, Helffer, Bernard
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