Results 31 to 40 of about 73,015 (248)
Mathematics, 2020 This paper is devoted to solving boundary value problems for differential equations with fractional derivatives by the Fourier method. The necessary information is given (in particular, theorems on the completeness of the eigenfunctions and associated ...
Temirkhan Aleroev
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Nodal sets and growth exponents of Laplace eigenfunctions on surfaces
, 2014 We prove a result, announced by F. Nazarov, L. Polterovich and M. Sodin that exhibits a relation between the average local growth of a Laplace eigenfunction on a closed surface and the global size of its nodal set.
Roy-Fortin, Guillaume
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Topological Properties of Neumann Domains [PDF]
, 2015 A Laplacian eigenfunction on a two-dimensional manifold dictates some natural partitions of the manifold; the most apparent one being the well studied nodal domain partition.
Band, Ram, Fajman, David
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Eigenfunction concentration via geodesic beams [PDF]
, 2020 In this article we develop new techniques for studying concentration of Laplace eigenfunctions $\phi_\lambda$ as their frequency, $\lambda$, grows. The method consists of controlling $\phi_\lambda(x)$ by decomposing $\phi_\lambda$ into a superposition of
Canzani, Yaiza, Galkowski, Jeffrey
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Advanced Photonics Research, EarlyView.This review highlights recent advances in accelerating luminescence in nanostructures through cooperative emission, resonator coupling, and nonlocal light–matter interactions. By unifying concepts such as excitonic superradiance, superfluorescence, and the plasmonic Purcell effect, it reveals physical limits of ultrafast emission and their potential ...
Masaaki Ashida +3 more
wiley +1 more source
Bound state eigenfunctions need to vanish faster than $|x|^{-3/2}$
, 2016 In quantum mechanics students are taught to practice that eigenfunction of a physical bound state must be continuous and vanishing asymptotically so that it is normalizable in $x\in (-\infty, \infty)$.
Ahmed, Zafar
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A microlocal approach to eigenfunction concentration [PDF]
, 2018 We describe a new approach to understanding averages of high energy Laplace eigenfunctions, $u_h$, over submanifolds, $$ \Big|\int _H u_hd\sigma_H\Big| $$ where $H\subset M$ is a submanifold and $\sigma_H$ the induced by the Riemannian metric on $M ...
Galkowski, Jeffrey
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Mathematical Prediction for Geometry‐Mediated Cell 3D In‐Growth on Bone Tissue Engineering Scaffolds
Advanced Science, EarlyView.This study identifies a fundamental pore size dependent pattern of three dimensional bone marrow derived mesenchymal stem cell (BMSC) infiltration within porous scaffolds, where small pores promote horizontal cellular bridging and large pores facilitate vertical migration.
Xiang Gao +15 more
wiley +1 more source
Eigenfunctions in Finsler Gaussian solitons
Open Mathematics, 2023 Gaussian solitons are important examples in the theory of Riemannian measure space. In the first part, we explicitly characterize the first eigenfunctions of the drift Laplacian in a Gaussian shrinking soliton, which shows that apart from each coordinate
Liu Caiyun, Yin Songting
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Additional symmetries of constrained CKP and BKP hierarchies
, 2010 The additional symmetries of the constrained CKP (cCKP) and BKP (cBKP) hierarchies are given by their actions on the Lax operators, and their actions on the eigenfunction and adjoint eigenfunction $\{\Phi_i,\Psi_i \}$ are presented explicitly ...
A. Alexandrov +31 more
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