scholarly journals Spectral properties of the Neumann-Laplace operator in quasiconformal regular domains

2019 ◽  
pp. 129-144
Author(s):  
V. Gol’dshtein ◽  
V. Pchelintsev ◽  
A. Ukhlov
Keyword(s):  
Laplace Operator ◽  
Spectral Properties

scholarly journals p-Laplace Operators for Oriented Hypergraphs

2021 ◽  
Author(s):  
Jürgen Jost ◽  
Raffaella Mulas ◽  
Dong Zhang
Keyword(s):  
Laplace Operator ◽  
Spectral Properties ◽  
General Setting ◽  
Laplace Operators

AbstractThe p-Laplacian for graphs, as well as the vertex Laplace operator and the hyperedge Laplace operator for the general setting of oriented hypergraphs, are generalized. In particular, both a vertex p-Laplacian and a hyperedge p-Laplacian are defined for oriented hypergraphs, for all p ≥ 1. Several spectral properties of these operators are investigated.

scholarly journals Spectral properties of the Neumann–Poincaré operator and cloaking by anomalous localized resonance for the elasto-static system

2017 ◽  
Vol 29 (2) ◽  
pp. 189-225 ◽  
Author(s):  
KAZUNORI ANDO ◽  
YONG-GWAN JI ◽  
HYEONBAE KANG ◽  
KYOUNGSUN KIM ◽  
SANGHYEON YU
Keyword(s):  
Laplace Operator ◽  
Spectral Properties ◽  
Static System ◽  
Two Dimensional ◽  
Eigenvalues And Eigenfunctions ◽  
Lamé System ◽  
Accumulation Points ◽  
Lame System ◽  
The Laplace Operator

We first investigate spectral properties of the Neumann–Poincaré (NP) operator for the Lamé system of elasto-statics. We show that the elasto-static NP operator can be symmetrized in the same way as that for the Laplace operator. We then show that even if elasto-static NP operator is not compact even on smooth domains, it is polynomially compact and its spectrum on two-dimensional smooth domains consists of eigenvalues that accumulate to two different points determined by the Lamé constants. We then derive explicitly eigenvalues and eigenfunctions on discs and ellipses. Using these resonances occurring at eigenvalues is considered. We also show on ellipses that cloaking by anomalous localized resonance takes place at accumulation points of eigenvalues.

scholarly journals Fractional Laplace operator in two dimensions, approximating matrices, and related spectral analysis

CALCOLO ◽  
2020 ◽  
Vol 57 (3) ◽  
Author(s):  
Lidia Aceto ◽  
Mariarosa Mazza ◽  
Stefano Serra-Capizzano
Keyword(s):  
Spectral Analysis ◽  
Laplace Operator ◽  
Spectral Properties ◽  
Numerical Experiments ◽  
Two Dimensions ◽  
Spatial Variables ◽  
The Matrix ◽  
Constant Coefficients ◽  
Fractional Laplace Operator ◽  
Concise Description

Abstract In this work we review some proposals to define the fractional Laplace operator in two or more spatial variables and we provide their approximations using finite differences or the so-called Matrix Transfer Technique. We study the structure of the resulting large matrices from the spectral viewpoint. In particular, by considering the matrix-sequences involved, we analyze the extreme eigenvalues, we give estimates on conditioning, and we study the spectral distribution in the Weyl sense using the tools of the theory of Generalized Locally Toeplitz matrix-sequences. Furthermore, we give a concise description of the spectral properties when non-constant coefficients come into play. Several numerical experiments are reported and critically discussed.

scholarly journals Spectral properties of the generalised Samarskii-Ionkin type problems

Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 1019-1024
Author(s):  
Nurgissa Yessirkegenov
Keyword(s):  
Boundary Conditions ◽  
Explicit Form ◽  
Laplace Operator ◽  
Spectral Properties ◽  
The Laplace Operator

In this paper, we study spectral properties of the Laplace operator with generalised Samarskii-Ionkin boundary conditions in a disk. The eigenfunctions and eigenvalues of these problems are constructed in the explicit form. Moreover, we prove the completeness of these eigenfunctions

Model of multicomponent narrow-band periodical non-stationary random signal

2020 ◽  
Vol 2020 (48) ◽  
pp. 17-24
Author(s):  
I.M. Javorskyj ◽  
◽  
R.M. Yuzefovych ◽  
P.R. Kurapov ◽  
◽  
...  
Keyword(s):  
Time Series ◽  
Real Time ◽  
Hilbert Transform ◽  
Spectral Properties ◽  
Narrow Band ◽  
Analytic Signal ◽  
Random Signal ◽  
Hilbert Transformation ◽  
The Hilbert Transform

The correlation and spectral properties of a multicomponent narrowband periodical non-stationary random signal (PNRS) and its Hilbert transformation are considered. It is shown that multicomponent narrowband PNRS differ from the monocomponent signal. This difference is caused by correlation of the quadratures for the different carrier harmonics. Such features of the analytic signal must be taken into account when we use the Hilbert transform for the analysis of real time series.

Structure and Spectral Properties of New Composites Based on Metal Alkanoates with Gold Nanoparticles

2015 ◽  
Vol 60 (04) ◽  
pp. 356-361 ◽  
Author(s):  
A. Tolochko ◽  
◽  
P. Teselko ◽  
A. Lyashchova ◽  
D. Fedorenko ◽  
...  
Keyword(s):  
Gold Nanoparticles ◽  
Spectral Properties
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