scholarly journals Dynamics of Nodal Points and the Nodal Count on a Family of Quantum Graphs

2011 ◽  
Vol 13 (1) ◽  
pp. 145-184 ◽  
Author(s):  
Ram Band ◽  
Gregory Berkolaiko ◽  
Uzy Smilansky
Keyword(s):  
Quantum Graphs ◽  
Nodal Count ◽  
Nodal Points

scholarly journals Stability of eigenvalues of quantum graphs with respect to magnetic perturbation and the nodal count of the eigenfunctions

2014 ◽  
Vol 372 (2007) ◽  
pp. 20120522 ◽  
Author(s):  
Gregory Berkolaiko ◽  
Tracy Weyand
Keyword(s):  
Magnetic Field ◽  
Morse Index ◽  
Magnetic Potential ◽  
Zero Magnetic Field ◽  
Quantum Graphs ◽  
Nodal Count ◽  
Magnetic Perturbation ◽  
Number Of Zeros ◽  
Stability Of Eigenvalues ◽  
The Stability

We prove an analogue of the magnetic nodal theorem on quantum graphs: the number of zeros ϕ of the n th eigenfunction of the Schrödinger operator on a quantum graph is related to the stability of the n th eigenvalue of the perturbation of the operator by magnetic potential. More precisely, we consider the n th eigenvalue as a function of the magnetic perturbation and show that its Morse index at zero magnetic field is equal to ϕ −( n −1).

Tolerance is theoretical and practical principles

1996 ◽  
pp. 13-23
Author(s):  
Mykhailo Babiy
Keyword(s):  
Religious Diversity ◽  
The Other ◽  
Nodal Points ◽  
Characteristic Features ◽  
The One ◽  
Ukrainian Society

Political ideological pluralism, religious diversity are characteristic features of modern Ukrainian society. On the one hand, multiculturalism, socio-political, religious differentiation of the latter appear as important characteristics of its democracy, as a practical expression of freedom, on the other - as a factor that led to the deconsocialization of society, gave rise to "nodal points" of tension, confrontational processes, in particular, in political and religious spheres.

GIS Technologies in Course of Mathematical Cartography

2017 ◽  
Vol 921 (3) ◽  
pp. 30-35
Author(s):  
N.G. Ivlieva ◽  
V.F. Manukhov
Keyword(s):  
Software Tools ◽  
Digital Models ◽  
Map Projection ◽  
Gis Technologies ◽  
Surface Distortion ◽  
Nodal Points ◽  
Projection Properties ◽  
Special Software

GIS are closely related to mathematical cartography, as they work with spatially coordinated data. Practical course in mathematical cartography should meet the requirements of time and include tasks involving the use of modern GIS technologies. The functionality of GIS packages allow you to easily create maps in a given map projection, draw graticules and measured grids, perform dimensions on maps. This article is devoted to the research of map projection properties on the basis of GIS technologies in a practical course of mathematical cartography. The focus is on visual way to display local and regional distortions on maps. To create lines of equal distortion should use special software tools that allow to build digital models of surface distortion distribution directly on formulas or be interpolated both discretely located nodal points and isolines.

scholarly journals Average scattering entropy of quantum graphs

2021 ◽  
Vol 103 (6) ◽  
Author(s):  
Alison A. Silva ◽  
Fabiano M. Andrade ◽  
Dionisio Bazeia
Keyword(s):  
Quantum Graphs

scholarly journals Symmetry-protected nodal points and nodal lines in magnetic materials

2021 ◽  
Vol 103 (24) ◽  
Author(s):  
Jian Yang ◽  
Chen Fang ◽  
Zheng-Xin Liu
Keyword(s):  
Magnetic Materials ◽  
Nodal Lines ◽  
Nodal Points ◽  
Symmetry Protected

scholarly journals Chiralities of nodal points along high-symmetry lines with screw rotation symmetry

2021 ◽  
Vol 103 (23) ◽  
Author(s):  
Rafael González-Hernández ◽  
Erick Tuiran ◽  
Bernardo Uribe
Keyword(s):  
High Symmetry ◽  
Rotation Symmetry ◽  
Nodal Points

scholarly journals Dirac particles on periodic quantum graphs

2021 ◽  
Vol 104 (1) ◽  
Author(s):  
J. R. Yusupov ◽  
K. K. Sabirov ◽  
D. U. Matrasulov
Keyword(s):  
Quantum Graphs ◽  
Dirac Particles

scholarly journals Isoscattering strings of concatenating graphs and networks

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Michał Ławniczak ◽  
Adam Sawicki ◽  
Małgorzata Białous ◽  
Leszek Sirko
Keyword(s):  
Trace Function ◽  
Quantum Graphs ◽  
Mathematical Approach ◽  
Large Graphs ◽  
Graphs And Networks ◽  
Scattering Matrices ◽  
Theoretical Predictions ◽  
Infinite Strings ◽  
Microwave Networks ◽  
Insight Into

AbstractWe identify and investigate isoscattering strings of concatenating quantum graphs possessing n units and 2n infinite external leads. We give an insight into the principles of designing large graphs and networks for which the isoscattering properties are preserved for $$n \rightarrow \infty $$ n → ∞ . The theoretical predictions are confirmed experimentally using $$n=2$$ n = 2 units, four-leads microwave networks. In an experimental and mathematical approach our work goes beyond prior results by demonstrating that using a trace function one can address the unsettled until now problem of whether scattering properties of open complex graphs and networks with many external leads are uniquely connected to their shapes. The application of the trace function reduces the number of required entries to the $$2n \times 2n $$ 2 n × 2 n scattering matrices $${\hat{S}}$$ S ^ of the systems to 2n diagonal elements, while the old measures of isoscattering require all $$(2n)^2$$ ( 2 n ) 2 entries. The studied problem generalizes a famous question of Mark Kac “Can one hear the shape of a drum?”, originally posed in the case of isospectral dissipationless systems, to the case of infinite strings of open graphs and networks.

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