Zobrazeno 1 - 10
of 27
pro vyhledávání: '"Ram Band"'
Publikováno v:
Symmetry, Vol 11, Iss 2, p 185 (2019)
We consider stationary waves on nonlinear quantum star graphs, i.e., solutions to the stationary (cubic) nonlinear Schrödinger equation on a metric star graph with Kirchhoff matching conditions at the centre. We prove the existence of solutions that
Externí odkaz:
https://doaj.org/article/108f250d4ef445cdab71931b108244b6
Publikováno v:
Journal of Mathematical Analysis and Applications. 470:135-144
A foundational result in the theory of Lyndon words (words that are strictly earlier in lexicographic order than their cyclic permutations) is the Chen-Fox-Lyndon theorem which states that every word has a unique non-increasing decomposition into Lyn
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ac569ce236bf0d230d8303cc7b0cfdaa
https://doi.org/10.1016/j.jmaa.2018.09.058
https://doi.org/10.1016/j.jmaa.2018.09.058
An eigenfunction of the Laplacian on a metric (quantum) graph has an excess number of zeros due to the graph's non-trivial topology. This number, called the nodal surplus, is an integer between 0 and the graph's first Betti number $\beta$. We study t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cb957124d6cb9e111ee84f67fb1e8479
Autor:
August J. Krueger, Ram Band
Publikováno v:
Contemporary Mathematics. :129-154
The Sturm oscillation property, i.e. that the $n$-th eigenfunction of a Sturm-Liouville operator on an interval has $n -1$ zeros (nodes), has been well studied. This result is known to hold when the interval is replaced by a metric (quantum) tree gra
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2879a3c77389460733a46f1bbb19a89d
https://doi.org/10.1090/conm/717/14445
https://doi.org/10.1090/conm/717/14445
Autor:
Gal Shmuel, Ram Band
Publikováno v:
Journal of the Mechanics and Physics of Solids. 92:127-136
We show that the frequency spectrum of two-component elastic laminates admits a universal structure, independent of the geometry of the periodic-cell and the specific physical properties. The compactness of the structure enables us to rigorously deri
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f18ceb611f5bdaa30ab0ffdfde4acfac
https://doi.org/10.1016/j.jmps.2016.04.001
https://doi.org/10.1016/j.jmps.2016.04.001
Autor:
Ram Band, David Fajman
Publikováno v:
Annales Henri Poincaré. 17:2379-2407
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. An alternative partition is revealed by considering a set of distinguished
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::eedcd738d9a738bc28fbec4c9b3b8f9e
https://doi.org/10.1007/s00023-016-0468-7
https://doi.org/10.1007/s00023-016-0468-7
The Neumann points of an eigenfunction f on a quantum (metric) graph are the interior zeros of $$f'$$ . The Neumann domains of f are the sub-graphs bounded by the Neumann points. Neumann points and Neumann domains are the counterparts of the well-stu
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::56a219d3f37c2fa99717379303777bc6
Autor:
Guillaume Lévy, Ram Band
Publikováno v:
Annales Henri Poincare
Annales Henri Poincare, 2017, 18 (10), pp.3269-3323. ⟨10.1007/s00023-017-0601-2⟩
Annales Henri Poincare, 2017, 18 (10), pp.3269-3323. ⟨10.1007/s00023-017-0601-2⟩
A finite discrete graph is turned into a quantum (metric) graph once a finite length is assigned to each edge and the one-dimensional Laplacian is taken to be the operator. We study the dependence of the spectral gap (the first positive Laplacian eig
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::70df65337c4cf215565a049a5843fbff
https://hal.archives-ouvertes.fr/hal-01427968
https://hal.archives-ouvertes.fr/hal-01427968
It has been suggested that the distribution of the suitably normalized number of zeros of Laplacian eigenfunctions contains information about the geometry of the underlying domain. We study this distribution (more precisely, the distribution of the "
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c69e20f6a775d11ea7d7fa5c81bb1d37