Results 41 to 50 of about 48,454 (295)

On singularity and properties of eigenvectors of complex Laplacian matrix of multidigraphs

AKCE International Journal of Graphs and Combinatorics, 2023
In this article, we associate a Hermitian matrix to a multidigraph G. We call it the complex Laplacian matrix of G and denote it by [Formula: see text]. It is shown that the complex Laplacian matrix is a generalization of the Laplacian matrix of a graph.
Sasmita Barik, Sane Umesh Reddy, Gopinath Sahoo   +2 more
doaj   +1 more source

Geometry of the Laplacian

Linear Algebra and its Applications, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +3 more sources

Curvature and the eigenvalues of the Laplacian [PDF]

Journal of Differential Geometry, 1967
A famous formula of H. Weyl [17] states that if D is a bounded region of R d with a piecewise smooth boundary B, and if 0 > γ1 ≥ γ2 ≥ γ3 ≥ etc. ↓−∞ is the spectrum of the problem $$\displaystyle\begin{array}{rcl} \varDelta f =\big (\partial ^{2}/\partial x_{ 1}^{2} + \cdots + \partial ^{2}/\partial x_{ d}^{2}\big)f =\gamma f\quad \mbox{ in }D,& &{}\
McKean, Jr., H. P., Singer, I. M.
openaire   +4 more sources

Estimates of the Laplacian Spectrum and Bounds of Topological Invariants for Riemannian Manifolds with Boundary

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2019
We set out to obtain estimates of the Laplacian Spectrum of Riemannian manifolds with non-empty boundary. This was achieved using standard doubled manifold techniques. In simple terms, we pasted two copies of the same manifold along their common boundary
Sabatini Luca
doaj   +1 more source

The spectra of the Laplacian

Journal of Functional Analysis, 1991
The author considers the minimal and the maximal closed realization of the Laplacian on the half space and on the unit ball, starting from the set of compactly supported and infinitely differentiable functions. Then he describes completely the various spectra of these operators, and notices that they are drastically different from those in the whole ...
openaire   +2 more sources

On the Laplacian and fractional Laplacian in an exterior domain

Advances in Differential Equations, 2012
We see that the generalized Fourier transform due to A.G. Ramm for the case of $n=3$ space dimensions remains valid, with some modifications, for all space dimensions $n\ge 2$. We use the resulting spectral representation of the exterior Laplacian to study exterior problems. In particular the Fourier splitting method developed by M.E.
Kosloff, Leonardo, Schonbek, Tomas
openaire   +2 more sources

Investigation of 3D Wave Propagation in Foam‐Core Functionally Graded Material Magneto‐Piezoelectric Smart Nanoplates

Advanced Engineering Materials, EarlyView.
This study reveals how wave propagation in FG‐MEE nanoplates can be tuned via material gradients, porosity, and external fields. Using NSGT and Hamilton's principle, analytical solutions capture key dispersion behaviors. Findings highlight the potential of smart nanoplates for adaptive control in high‐performance applications like sonar and aerospace ...
Mustafa Buğday, Ismail Esen
wiley   +1 more source

On the $ A_{\alpha^-} $-spectra of graphs and the relation between $ A_{\alpha} $- and $ A_{\alpha^-} $-spectra

AIMS Mathematics
Let $ G $ be a graph with adjacency matrix $ A(G) $, and let $ D(G) $ be the diagonal matrix of the degrees of $ G $. For any real number $ \alpha\in [0, 1] $, Nikiforov defined the $ A_{\alpha} $-matrix of $ G $ as $ A_{\alpha}(G) = \alpha D (G) +
Wafaa Fakieh, Zakeiah Alkhamisi, Hanaa Alashwali   +2 more
doaj   +1 more source

Cospectral constructions for several graph matrices using cousin vertices

Special Matrices, 2021
Graphs can be associated with a matrix according to some rule and we can find the spectrum of a graph with respect to that matrix. Two graphs are cospectral if they have the same spectrum.
Lorenzen Kate
doaj   +1 more source

The Laplacian eigenvalues of a polygon [PDF]

Computers & Mathematics with Applications, 2004
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Pavel Grinfeld, Gilbert Strang
openaire   +2 more sources