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A geometric bound on the lowest magnetic Neumann eigenvalue via the torsion function
We obtain an upper bound on the lowest magnetic Neumann eigenvalue of a bounded, convex, smooth, planar domain with moderate intensity of the homogeneous magnetic in terms of the torsion function and of the lowest magnetic ...
Applied mathematics
- 2024 •
- Jimp •
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Spectral isoperimetric inequalities for Robin Laplacians on 2-manifolds and unbounded cones
We consider the problem of geometric optimization of the lowest eigenvalue isoperimetric inequality holds for the lowest eigenvalue of the Dirichlet-to-Neumann, the lowest Robin eigenvalue is maxi...
Pure mathematics
- 2022 •
- Jimp •
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Optimization of the lowest eigenvalue for leaky star graphs
We consider the problem of geometric optimization for the lowest eigenvalue of the two-imensional Schrödinger operator with an attractive delta-interaction of a fixed strength, the support of which is a star graph with finitely many...
Pure mathematics
- 2018 •
- C •
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C - Kapitola v odborné knize
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Spectral Isoperimetric Inequality for the Delta' -Interaction on a Contour
We consider the problem of geometric optimization for the lowest eigenvalue of the two-dimensional Schrödinger operator with an attractive Delta'-interaction of a fixed strength, the support of which is a C2-smooth contour. Under th...
Pure mathematics
- 2021 •
- C •
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C - Kapitola v odborné knize
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Optimization of the lowest eigenvalue of a soft quantum ring
results for its lowest eigenvalue. For the first one, we fix mu(perpendicular to) and maximize the lowest eigenvalue with respect to shape of the curvilinear strip the lowest eigenvalue with resp...
Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
- 2021 •
- Jimp •
- Link
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Optimization of the lowest eigenvalue for leaky star graphs
We consider the problem of geometric optimization for the lowest eigenvalue of the two-dimensional Schriidinger operator with an attractive (5 interaction of a fixed strength, the support of which is a star graph with finitely many ...
Mathematics
- 2018 •
- D •
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D - Stať ve sborníku
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Reverse Isoperimetric Inequality for the Lowest Robin Eigenvalue of a Triangle
We consider the Laplace operator on a triangle, subject to attractive Robin boundary conditions. We prove that the equilateral triangle is a local maximiser of the lowest eigenvalue among all triangles of a given area provided that ...
Applied mathematics
- 2023 •
- Jimp •
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Numerical optimisation of Dirac eigenvalues
constraints. We consider the three lowest positive eigenvalues and their ratios. Roughly, a new, mass-dependent upper bound to the lowest eigenvalue in rectangles is proved existing or state new conjectures in the...
Pure mathematics
- 2024 •
- Jimp •
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Spectral isoperimetric inequalities for singular interactions on open arcs
We consider the problem of geometric optimization for the lowest eigenvalue of the two-dimensional Schrodinger operator with an attractive -interaction supported on an open arc with two free endpoints. Under a constraint of fixed le...
Applied mathematics
- 2019 •
- Jimp •
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The Lichnerowicz-Type Laplacians: Vanishing Theorems for Their Kernels and Estimate Theorems for Their Smallest Eigenvalues
In the present paper, we prove several vanishing theorems for the kernel of the Lichnerowicz type Laplacian and provide estimates for its lowest eigenvalue on closed Riemannian manifolds. As an example of the Lichnerowicz-type Lapla...
Pure mathematics
- 2024 •
- Jimp •
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